A general theorem on necessary conditions in optimal control

Francis Clarke

doi:10.3934/dcds.2011.29.485

Article Contents

2011, Volume 29, Issue 2: 485-503. Doi: 10.3934/dcds.2011.29.485

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A general theorem on necessary conditions in optimal control

Francis Clarke^1,

1.
Université de Lyon, Institut Camille Jordan, CNRS UMR 5208, 69622 Villeurbanne

Received: August 31, 2009

Revised: February 28, 2010

Published: May 2011

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Abstract

We give a relatively short and self-contained proof of a theorem that asserts necessary conditions for a general optimal control problem. It has been shown that this theorem, which is simple to state, provides a powerful template from which necessary conditions for various other problems in dynamic optimization can be directly derived, at the level of the state of the art. These include various extensions of the Pontryagin maximum principle and the multiplier rule.

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Mathematics Subject Classification: Primary: 49K15; Secondary: 49K21.

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References

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